Dynamical analysis of a non-linear difference equation

Abstract

In this article, we investigate the dynamics of the solutions of the following non-linear difference equation xn+1 = xn-2xn-3 - 1; n ? ?0 with arbitrary initial conditions x-2; x-1; x0. Besides, we have studied peri- odic behaviours of related difference equation especially asymptotic periodicity and eventually periodicity. Then, we have researched unbounded solutions of difference equation. © 2019 by Eudoxus Press,LLC,all rights reserved.